Methods and systems for performing model-based image processing

ABSTRACT

Methods and systems for model-based image processing are provided. One method includes selecting at least one reference image from a plurality of reference images, partitioning the at least one reference image into a plurality of patches, generating a probability distribution for each of the patches, and generating a model of a probability distribution for the at least one reference image using the probability distributions for each of the patches.

BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates generally to imaging systemsand more particularly, to methods and systems for performing model-basediterative reconstruction of images acquired from a computed tomography(CT) imaging system.

Traditionally, images have been reconstructed from Computed Tomography(CT) data using direct reconstruction algorithms such as filteredbackprojection. Recently, model based iterative reconstruction (MBIR)algorithms have been utilized to reconstruct CT images. For example, inapplications such as dual energy CT reconstruction, the reconstructedimage corresponds to the decomposition of the object into materialcomponents, wherein each specific material has its own distinctivespatial structure, texture, and distribution.

Markov random fields (MRFs) have been used in MBIR algorithms fortomographic image reconstruction. MRFs provide a simple and generallyeffective method to model the spatial texture in the images. Inoperation, MRFs are used to model the spatial texture of an image bycalculating a gradient between each pixel in the image and the neighborssurrounding the pixels. However, MRFs are not enabled to modelproperties of the image that correspond to the actual values of thepixel. More specifically, MRFs do not model pixel density values thatare based on the actual value or magnitude of the pixels. Rather, MRFmodels, model the pixels based on the local gradient between the pixeland their neighbors. As a result, it may be difficult to distinguish thevarious material components in the image. For example, the pixelintensity values are generated based on Hounsfield units. DifferentHounsfield units are assigned to each pixel based on the property of thematerials being images. Accordingly, it may be difficult to distinguishmaterials such as bones from other materials such as soft tissue whendesigning MRF models. Moreover, it is often difficult to estimate thevarious parameters utilized in the MRFs. As a result, the MRFs are lesseffective in capturing the subtle characteristics of complex images.

BRIEF DESCRIPTION OF THE INVENTION

In one embodiment, a method of generating a model for image processingis provided. The method includes selecting at least one reference imagefrom a plurality of reference images, partitioning the at least onereference image into a plurality of patches, generating a probabilitydistribution for each of the patches, and generating a model of aprobability distribution for the at least one reference image using theprobability distributions for each of the patches.

In another embodiment, a non-transitory computer readable medium isprovided. The non-transitory computer readable medium is programmed toinstruct a computer of a Computed Tomography (CT) system to receive auser input selecting at least one reference image from a plurality ofreference images, automatically partition the at least one referenceimage into a plurality of patches, and generate a probabilitydistribution for each of the patches. The computer readable medium isalso programmed to generate a model of a probability distribution forthe at least one reference image using the probability distributions foreach of the patches.

In a further embodiment, a computed tomography (CT) imaging system isprovided. The CT imaging system includes a detector configured to outputx-ray attenuation information and a processor coupled to the detector.The processor is configured to receive the x-ray attenuation informationand receive a user input selecting at least one reference image from aplurality of reference images, automatically partition the at least onereference image into a plurality of patches, and generate a probabilitydistribution for each of the patches. The processor is furtherconfigured to generate a model of a probability distribution for the atleast one reference image using the probability distributions for eachof the patches.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified block diagram of an imaging system formed inaccordance with various embodiments.

FIG. 2 is a flowchart illustrating a method of generating a model forreconstructing a plurality of images in accordance with variousembodiments.

FIG. 3 is a reference image that may be selected in accordance withvarious embodiments.

FIG. 4 illustrates a plurality of patches that may be formed inaccordance with various embodiments.

FIGS. 5A-5D illustrate a method of calculating a geometric mean for asingle patch in accordance with various embodiments.

FIG. 6 is a pictorial view of an exemplary imaging system formed inaccordance with various embodiments.

DETAILED DESCRIPTION OF THE INVENTION

The foregoing summary, as well as the following detailed description ofcertain embodiments will be better understood when read in conjunctionwith the appended drawings. To the extent that the figures illustratediagrams of the functional blocks of various embodiments, the functionalblocks are not necessarily indicative of the division between hardwarecircuitry or software components. Thus, for example, one or more of thefunctional blocks (e.g., processors or memories) may be implemented in asingle piece of hardware (e.g., a general purpose signal processor orrandom access memory, hard disk, or the like) or multiple pieces ofhardware. Similarly, the programs may be stand alone programs, may beincorporated as subroutines in an operating system, may be functions inan installed software package, and the like. It should be understoodthat the various embodiments are not limited to the arrangements andinstrumentality shown in the drawings.

As used herein, an element or step recited in the singular and proceededwith the word “a” or “an” should be understood as not excluding pluralof said elements or steps, unless such exclusion is explicitly stated.Furthermore, references to “one embodiment” are not intended to beinterpreted as excluding the existence of additional embodiments thatalso incorporate the recited features. Moreover, unless explicitlystated to the contrary, embodiments “comprising” or “having” an elementor a plurality of elements having a particular property may includeadditional such elements not having that property.

Also as used herein, the term “reconstructing” or “rendering” an imageor data set is not intended to exclude embodiments in which datarepresenting an image is generated, but a viewable image is not.Therefore, as used herein the term “image” broadly refers to bothviewable images and data representing a viewable image. However, manyembodiments generate, or are configured to generate, at least oneviewable image.

Various embodiments provide systems and methods for generating a modelwhich may be used to reconstruct computed tomographic (CT) images. Ingeneral, the model is embodied as a Gaussian Mixture Markov RandomFields (GM-MRF) model that is configured to model the density of thepixels and also concurrently model the spatial structure of the pixels.For example, in operation a reference image is selected. The referenceimage includes a plurality of pixels. A patch is generated for each ofthe plurality of pixels in the reference image. A probabilitydistribution is calculated for each individual patch. The probabilitydistributions for the plurality of patches are then combined by takingthe geometric mean to form a single probability distribution model forthe reference image.

Thus, in operation the GM-MRF model is configured to generate aplurality of individual patch models by jointly modeling the patchdensity and the spatial structure and texture of each patch, which is ofparticular importance for applications such as single and dual energy CTreconstruction. More specifically, each of the mixture components of theGM-MRF model specifies the mean of a particular patch, which in generalcorresponds to a particular material having a distinctive spatialstructure in the CT images. Moreover, each of the mixture components ofthe GM-MRF model also specifies an inverse covariance for the patch,which provides information that reflects the particular statisticalbehavior of each patch because the eigenvalues of the inverse covarianceare inversely proportional to the variances of the correspondingelements in the mixture component. During image reconstruction, theGM-MRF model can be used to control the regularization for theparticular patch. Additionally, the GM-MRF model includes easilyestimated parameters that are generated by merging the local patchmodels. More specifically, the GM-MRF model has an exact parameter,which provides information on a quantity of possible filings of theplane given the patch formulation in order to maintain the same energyafter merging from the local patch models. In operation, the parametersof the GM-MRF model may be estimated using, for example, Gaussianmixture parameter estimation, which enables accurate modeling of thelocal patches with expressive Gaussian mixture model, while theparameter estimation is still computationally tractable. In variousembodiments, the GM-MRF model also provides a framework for computingmaximum a posteriori (MAP) estimates that are based onmajorization-minimization using surrogate functions. Construction ofexact surrogate functions for the energy function results in a sequenceof quadratic optimizations, which makes the solution computationallytractable.

FIG. 1 illustrates a simplified block diagram of an exemplary imagingsystem 10 that is formed in accordance with various embodiments. Theimaging system 10 may be embodied as a dual-energy CT imaging system, asingle energy CT imaging system, or any other type of imaging system.The imaging system 10 includes an x-ray source 12 and a detector 14 thatare used to scan a subject 16. A computer 18 processes the acquiredinformation received from the detector 14 and prepares a plurality oftwo-dimensional (2D) images 20 that may be displayed on a display 22. Itshould be realized that any quantity of 2D images 20 may be displayed onthe display 22. In the exemplary embodiment, each of the 2D images 20represents a slice through a 3D volume dataset 24 at a specificlocation, or a volume rendering. The 3D volume dataset 24 may bedisplayed concurrently with or separately from the 2D images 20. Theimaging system 10 also includes a model generating module 30 that isprogrammed to automatically generate a model for reconstructing theimages 20 as is described in more detail below. In some embodiments, themodel generating module 30 may be formed as part of the computer 18 asshown in FIG. 1. Optionally, the model generating module 30 may beformed separately from the computer 18.

The model generating module 30 is configured to implement variousmethods described herein. The model generating module 30 may beimplemented as a piece of hardware that is installed in the computer 40.Optionally, the model generating module 30 may be implemented as a setof instructions that are installed on the computer 18. The set ofinstructions may be stand alone programs, may be incorporated assubroutines in an operating system installed on the computer 18, may befunctions in an installed software package on the computer 18, and thelike. It should be understood that the various embodiments are notlimited to the arrangements and instrumentality shown in the drawings.

The imaging system 10 also includes a user interface 26 that allows anoperator to enter data, enter and change scanning parameters, accessprotocols, measure structures of interest, and the like. The userinterface 26 also enables the operator to transmit and receiveinformation to and/or from the processor 18 and/or the module 30 thatinstructs the processor 18 and/or the module 30 to perform the variousmethods described herein.

FIG. 2 is a flowchart illustrating a method 100 for generating a modelfor reconstructing an image. In various embodiments, the method 100 maybe implemented using either the processor 18 or the module 30 both shownin FIG. 1. It should be noted that although the method 100 is describedin connection with a CT imaging system having particularcharacteristics, such as the CT imaging system 10 shown in FIG. 1, thevarious embodiments described herein are not limited to CT imaging or toany particular imaging characteristics. For example, although the method100 is described in connection with images acquired using a dual-energyCT imaging system as shown in FIG. 1, the method 100 may also beutilized to model images acquired using a single energy CT imagingsystem or any other type of imaging system.

The method 100 includes accessing at 102 with a processor, such as theprocessor 18 shown in FIG. 1, a 3D volume dataset, such as the 3D volumedataset 24, also shown in FIG. 1. In the exemplary embodiment, the 3Dvolume dataset 24 includes a sequence of N two-dimensional (2D) images20 of the subject 16. In one embodiment, the 3D volume dataset 24 mayinclude grayscale data, scalar grayscale data, parameters or componentssuch as color, displacement, velocity, temperature, density,concentration, material strain or other information or source ofinformation that may be coded into an image. The 2D images 20 may beacquired over the duration of a patient scan, for example. The quantityof 2D images 20 may vary from patient to patient and may depend upon thelength of the individual patient's scan as well as the flame rate of theimaging system 10.

In the exemplary embodiment, the 2D images 20 are acquired sequentiallyduring a single scanning procedure. Therefore, the 2D images 20 are ofthe same subject or patient 16, but acquired at different times duringthe same scanning procedure. Thus, in the exemplary embodiment, theplurality of 2D images 20 includes images acquired at different timeperiods during the scanning procedure. It should therefore be realizedthat in the exemplary embodiment, the 3D volume dataset 24 includes morethan the two 2D images 20.

At 104 one or more reference images 200 are selected from the pluralityof reconstructed images 20. In some embodiments, a volume of images(e.g., 3D volume) may be selected. FIG. 3 illustrates the exemplaryreference image 200 that may be selected at 104. It should be realizedthat any one or more of the 2D images 20 may be selected as thereference image 200. As shown in FIG. 3, the reference image 200 isformed from a plurality of pixels labeled 210 a . . . 210 n.

At 106, the reference image 200 is partitioned or divided into aplurality of non-overlapping blocks or patches 220 a . . . 220 n,respectively, as shown in FIG. 4 that cover a plane of the referenceimage 200. As used herein, the term “tile” refers to a single patch 220.Additionally, the term “tiling” refers to partitioning the referenceimage 200 such that the plurality of patches 220 or tiles, are arrangedin a pattern on the reference image 200 to form an array of patches 220that is analogous to floor tiles.

For example, as shown in FIG. 4, the reference image 200 has a width 240and a length 242 that define a plane 244 of the reference image 200. Inthe illustrated embodiment, each of the patches 220 is sized as a square2×2 matrix of pixels 210. More specifically, in the illustratedembodiment, each of the patches 220 a . . . 220 n is formed as a 2×2matrix that includes four adjacent pixels 210. Therefore, in theillustrated embodiment, the plane 244 of the reference image 200 iscovered with an array of patches 220, wherein each patch 220 includesfour pixels. However, it should be realized that although FIG. 4illustrates the reference image 200 being partitioned into an array of2×2 patches 220 that cover the plane 244, the reference image 200 may bepartitioned into patches of any size and shape. For example, each of thepatches 220 may be formed as a 3×3 patch such that the plane 244 of thereference image 200 is covered by an array of patches, wherein eachpatch 220 includes nine pixels. In various embodiments, each of thepatches 220 may be formed as a 3×4 patch, a 4×4 patch, a 4×5 patch, a5×5 patch, etc. It should be appreciated that different dimensions ofpatch sizes may be provided. In some embodiments, 3D patches may beprovided, for example, a 2×2×2 patch, a 2×2×3 patch, a 2×3×3 patch, a3×3×3 patch, etc. It should be noted that various embodiments may beapplied to 2D image slices and/or 3D image volume (e.g., reconstruct anentire volume instead of generating slice by slice).

Referring again to FIG. 2, at 108 an initial patch is selected from theplurality of patches 220. For example, a patch 230, shown in FIG. 4 maybe selected. At 110, a probability distribution is calculated for theselected patch 230. It should be realized that the term probabilitydistribution may include a geometric mean, an inverse covariance matrix,and one or more parameters. Thus, in various embodiments, the followingare calculated: a mean vector (μ), an inverse covariance (B matrix), andone or more parameters (which in various embodiments is the sum of acombination of parameters, or which in various embodiment is the mixtureprobability parameter (π)).

For example, let x be the reference image 200 with pixels sεS, where Sis the set of all pixels 210 in the reference image 200. Moreover, letz_(s) be a patch, such as the patch 230 in the reference image 200 withthe pixel s at the upper left corner. Thus, the patch z_(s) may bedefined as z_(s)={x_(r): rεs+W} where W is a window of p pixels which isthe illustrated embodiment is four pixels 210.

For example, as described above each of the patches 220 are arrangedadjacent to each other such that the patches abut against each other ina non-overlapping pattern. Optionally, the patches may partially overlapeach other. Accordingly, each patch, such as the patch 230, may bemodeled as having a multivariate Gaussian mixture distribution with Ksubclasses in accordance with:

$\begin{matrix}{{g\left( z_{s} \right)} = {\sum\limits_{k = 0}^{K - 1}{\pi_{k}\frac{1}{\left( {2\pi} \right)^{p}}{B_{k}}^{\frac{1}{2}}\exp\left\{ {{- \frac{1}{2}}{{z_{s} - \mu_{k}}}\frac{2}{B_{k}}} \right\}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where the parameters πk, μk, Bk represent the mixture probability, mean,and inverse covariance of the subclass k, respectively. Moreover, assumethat S0, . . . , Sη−1 is a set of all pixels within the patch 230 afterbeing partitioned into η sets, wherein each of the η sets cover theplane 244 of the image 200. More specifically, assume that {z_(s)}, sεSmincludes all the pixels in x. For example, in one embodiment each zs maybe a square patch formed as an M×M matrix of pixels and the set ofpatches {z_(s)}, sεSm tile the plane 244. Accordingly, in operation togenerate the multivariate Gaussian mixture distribution of the patch230, the patch 230 is shifted in the X and Y positions. Thus, any set ofpatches 230 may be used to encompass or tile the image plane (2D) orimage volume (3D) or any set of shifted patches may be used to encompassor tile the image plane (2D) or image volume (3D). It should be notedthat different patch tiling with the same patch size or different patchsize may be used. For example, η defines the number of differentpossibilities and the patch 230 may be shifted in different directions.For example, for a 2×2 patch, the patch may be shifted by half a tile(or patch dimension) up, down, left, and/or right as viewed in FIGS.5A-5D described below.

Thus, in some embodiments, the methods described herein may be utilizedto generate a global image model that may be utilized to reconstruct avariety of images. As used herein, the term global image model refers toa prior model that may be utilized to reconstruct or process a varietyof images. To generate the global image model, the image is partitionedinto a plurality of patches that tile the plane in a first arrangement.For example, and referring again to FIG. 4, it should be realized thatthe reference image 200 may be partitioned into various arrangements ofpatches. For an array of 2×2 patches there are four distinct tilingarrangements that may be used to partition the reference image 200. Forexample, the array of patches may be shifted side-to-side in theX-direction or shifted up and/or down in the Y-direction. Accordingly,to generate the prior global model, a prior model, such as the GM-MRFmodel is generated for each of the tiling arrangements. In this example,four GM-MRF models are generated. The global model is then generated bycalculating the geometric average of the distributions of all possiblefilings, which in this case are four possible filings. Thus, in thisembodiment, the prior global model is generated by calculating ageometric average for each of the filings, and then calculating ageometric average using the four geometric averages calculated for eachpossible tiling. In some embodiments the geometric mean of all possiblefilings may be used to improve modeling.

For example, FIG. 5A illustrates the patch 230 shifted along an X-axisin a first direction to define a first non-local patch 250. FIG. 5Billustrates the patch 230 shifted along the X-axis in a second directionto define a second non-local patch 252. FIG. 5C illustrates the patch230 shifted along a Y-axis in a first direction to define a thirdnon-local patch 254. FIG. 5D illustrates the patch 230 shifted along theY-axis in a second direction to define a fourth non-local patch 256.Accordingly, the Gaussian mixture distribution is calculated for thepatch 230 at the four different positions, shown in FIGS. 5A-5D inaccordance with Equation 1. More specifically, a Gaussian probabilitydistribution is calculated for the first non-local patch 250, the secondnon-local patch 252, the third non-local patch 254, and the fourthnon-local patch 256. The geometric mean for the Gaussian mixturedistributions patch 230 is then calculated in accordance withEquation 1. It should be noted that in various embodiments, the modelingof the patches and patch distribution includes the calculation of themean, but also the inverse covariance and the mixture probabilityparameter as described herein (and as illustrated in FIG. 1). Thus, invarious embodiments, all of these components are calculated from the oneor more reference images in order to form one or more models (e.g.,GM-MRF model).

Moreover, the distribution of the all the patches 220 forming thereference image 200 may be modeled as the product of the distributionfor each patch in accordance with:

$\begin{matrix}{{{Pm}(x)} = {{\prod\limits_{s \in S_{m}}{g\left( z_{s} \right)}} = {\exp\left\{ {- {\sum\limits_{s \in S_{m}}{V\left( z_{s} \right)}}} \right\}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where V (z_(s))=−log {g(z_(s))}. In this case, p_(m)(x) is a properdistribution that has the desired distribution for each patch 220.

Referring again to FIG. 2, in various embodiments, steps 108 and 110 areiteratively repeated for each of the patches 220. For example, asubsequent patch 232 may be selected 108 as shown in FIG. 4. The mean,an inverse covariance matrix, and/or one or more parameters of the patch232 are then calculated in accordance with Equations 1 and 2 asdescribed above with respect to the patch 230. Thus, at 112 the module30 determines whether a mean has been calculated for each of the patches220. Accordingly, steps 108 and 110 are iteratively repeated until amean is calculated for each of the patches 220 forming the referenceimage 200.

In operation, the discrete tiling of the plane, i.e. the reference image200, may introduce artificial boundaries between the non-overlappingpatches 220. For example, because the plane 244 of the reference image200 is tiled with a plurality of non-overlapping patches 220, theboundaries between the patches 220 may result in artifacts that mayreduce the texture quality of the reconstructed image. Accordingly, invarious embodiments, to remove potential artifacts that may occurbetween the boundaries defined between the separate patches 220, andthus improve the texture of the reference image 200, the method 100further includes calculating at 114 the geometric mean of each of thepossible tilings for the reference image 200 to determine the followingdistribution:

$\begin{matrix}{{p(x)} = {{\frac{1}{z}\left( {\prod\limits_{m = 0}^{n - 1}{P_{m}(x)}} \right)^{1/n}} = {\frac{1}{z}\exp\left\{ {{- \frac{1}{\eta}}{\sum\limits_{s \in S}{V\left( z_{s} \right)}}} \right\}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

where the normalizing constant z is utilized to assure that p(x) is aproper distribution after the geometric mean is computed usingEquation 1. It should be realized that the term η is equivalent to thequantity of pixels forming the patch 230. For example, in theillustrated embodiment, the patch 230 is formed as a 2×2 matrix ofpixels. Accordingly, in the illustrated embodiment, η=4. In anotherembodiment, the patch 230 may be formed as a 3×3 matrix of pixels.Accordingly, in this embodiment, η=9, etc. It should be noted that in a3D case, such as if the patch 230 is formed from a 3×3×3 matrix orpixels then η=27.

Referring again to FIG. 2, at 116, the Gaussian Mixture MRF (GM-MRF)model of the reference image 200 may be calculated in accordance with:

$\begin{matrix}{{V\left( z_{s} \right)} = {{- \log}\left\{ {\sum\limits_{k = 0}^{K - 1}{\pi_{k}\frac{1}{\left( {2\pi} \right)^{p}}{B_{k}}^{\frac{1}{2}}\exp\left\{ {- \frac{{{z_{s} - \mu_{k}}}_{B_{k}}^{2}}{2}} \right\}}} \right\}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Thus, the steps 102-116 generate one or more models (e.g., GM-MRF model)that may be used be subsequently used as described herein. The steps102-116 in various embodiments define a training process or method thatthat is performed on the reference image(s) (or reference volume) togenerate the one or more models. For example, the steps 102-116 invarious embodiment train the parameters (e.g., define the parameters)for use in image reconstruction or image processing.

At 118, the GM-MRF model calculated at 116 is utilized to process orreconstruct one or more images or is applied to one or more images.Thus, the reference image(s) are used to generate, for example, theGM-MRF model, which is then used on other sets of data. For example, theGM-MRF model may be used in an image reconstruction process whereinimage reconstruction of scan data or raw data (projection views) isperformed. As another example, the GM-MRF model may be used for imageprocessing, such as applying the GM-MRF model to one or more images(different than the reference images), such as for de-noising or forresolution improvement (e.g., removing image noise, or increasing imageedge sharpness).

In various embodiments, for example, the GM-MRF model calculated at 116may be utilized to calculate maximum a posteriori (MAP) estimates thatare used to perform image reconstruction at 118. To make the computationtractable, MAP reconstruction of images can be based onmajorization-minimization using surrogate functions as explained in moredetail below. In operation, construction of exact surrogate functionsfor the energy function result in a sequence of quadratic optimizationswhich enable the solution of the MAP function to be performed relativelyeasily.

In various embodiments, the MAP estimate of the GM-MRF model calculatedat 116 may be calculated in accordance with:

$\begin{matrix}\left. \hat{x}\leftarrow{\arg{\min\limits_{x}\left\{ {{- {{\log p}\left( y \middle| x \right)}} + {\frac{1}{\eta}{\sum\limits_{s \in S}{V\left( z_{s} \right)}}}} \right\}}} \right. & {{Equation}\mspace{14mu} 5}\end{matrix}$

where the parameters π_(k), μ_(k), B_(k) for each subclass k in Equation1 may be estimated using a conventional expectation maximization (EM)algorithm and V is the image volume. It should be noted that the MAPestimate is part of a training process or procedure described above.

In some embodiments, it may be difficult to calculate a directoptimization for the second term in Equation 5. Accordingly, in someembodiments, the second term in Equation 5 may be replaced with morecomputationally efficient function that is formed using a mixture ofquadratic functions.

For example, for the function

$\begin{matrix}{{u(x)} - {\frac{1}{\eta}{\sum\limits_{s \in S}{V\left( z_{s} \right)}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

where V (z_(s)) is defined by Equation 4, a quadratic function may bedefined in accordance with:

$\begin{matrix}{{u\left( {x;x^{\prime}} \right)} = {{\frac{1}{2\eta}{\sum\limits_{s \in S}{\sum\limits_{k = 0}^{K - 1}{{\overset{\sim}{w}}_{k}{{z_{s} - \mu_{k}}}_{B_{k}}^{2}}}}} + {c\left( x^{\prime} \right)}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

where x′ represents the current state of the image, and

$\begin{matrix}{{\overset{\sim}{w}}_{k} = \frac{\pi_{k}{B_{k}}^{\frac{1}{2}}\exp\left\{ {{- \frac{1}{2}}{{z_{s}^{\prime} - \mu_{k}}}_{B_{k}}^{2}} \right\}}{\sum\limits_{j = 0}^{K - 1}{\pi_{j}{B_{j}}^{\frac{1}{2}}\exp\left\{ {{- \frac{1}{2}}{{z_{s}^{\prime} - \mu_{j}}}_{B_{j}}^{2}} \right\}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

$\begin{matrix}{{c\left( x^{\prime} \right)} = {\frac{1}{\eta}{\sum\limits_{s\; ɛ\; S}\left\{ {{V\left( z_{s}^{\prime} \right)} - {\frac{1}{2}{\sum\limits_{k = 0}^{K - 1}{{\overset{\sim}{w}}_{k}{{z_{s}^{\prime} - \mu_{k}}}_{B_{k}}^{2}}}}} \right\}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

wherein z′_(s) represents a patch in x′. Accordingly, by utilizing anexemplary lemma, it may be shown that:u(x′;x′)=u(x)  Equation 10u(x;x′)≧u(x)  Equation 11

Thus, Equations 10 and 11 illustrate that u(x; x′) is a surrogatefunction for u(x) such that majorization-minimization methods may beutilized and a reduction of u(x; x′) ensures an equivalent reduction ofu(x).

As described above, a lemma may be utilized to define surrogatefunctions for logs of the exponential mixtures. In various embodiments,one exemplary lemma that may be utilized as described above is definedas

$\begin{matrix}{{f(x)} = {\sum\limits_{k}{w_{k}\exp\left\{ {- {v_{k}(x)}} \right\}}}} & {{Equation}\mspace{14mu} 12} \\{{q\left( {x;x^{\prime}} \right)}\overset{\bigtriangleup}{=}{{{- \log}\;{f\left( x^{\prime} \right)}} + {\sum\limits_{k}{{\overset{\sim}{\pi}}_{k}\left( {{v_{k}(x)} - {v_{k}\left( x^{\prime} \right)}} \right)}}}} & {{Equation}\mspace{14mu} 13} \\{{q\left( {x^{\prime};x^{\prime}} \right)} = {{- \log}\;{f\left( x^{\prime} \right)}}} & {{Equation}\mspace{14mu} 14} \\{{q\left( {x;x^{\prime}} \right)} \geq {{- \log}\;{f(x)}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Therefore, any optimization problem in the form:

$\begin{matrix}\left. \hat{x}\leftarrow{\arg{\min\limits_{x}\left\{ {{f(x)} + {u(x)}} \right\}}} \right. & {{Equation}\mspace{14mu} 16}\end{matrix}$

can be implemented as a sequence of optimizations as:

$\begin{matrix}{{repeat}\left\{ \hat{x}\leftarrow{\arg\;{\min\limits_{x}{\left\{ {{f\;(x)} + {u\left( {x;x^{\prime}} \right)}} \right\} x^{\prime}}}}\leftarrow\hat{x} \right\}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

where an optimization problem with quadratic priors is solved at eachiteration.

The various methods described herein provide a method of modeling thestatistical behavior of images. In one embodiment, the statisticalbehavior is modeled using a multivariate distribution of patches ofpixels formed in the image. Using a multivariate distribution of patchesof pixels enables the model to reconstruct images that include differentgray levels which represent different materials, such as air, bone,and/or soft tissue, which have different statistical behavior spatially.Therefore, in operation, the methods described herein model both thespatial distribution and the density together as a single multivariatedistribution. In dual energy systems, this may be referred to herein asmaterial decomposition because different materials have differentsignatures and behave differently.

In various embodiments, the models described herein are utilized toreconstruct or generally process CT images. Thus, the model providesuseful information as to the distribution of the image that correspondsto the CT data. The model also functions to sharpen the various featuresin the images by utilizing a statistical representation of the image.

More specifically, consider a partial image, e.g. a single pixel, thenconsider the relationship between the pixel and some of its neighbors.In one embodiment, a method of describing this relationship is a Markovrandom field (MRF). However, as described above the conventional MRFdoes not model the properties of the image that correspond to the actualvalues of the pixel to be modeled. Conventional MRF models only modelpixel-wise differences in the image. Whereas various methods describedherein model the differences between patch density and spatial structureand texture among patches. More specifically, the image is partiallymodeled based on the actual value or magnitude of the pixels by modelingthe distribution of the gray level in the patches and also the texturein the patches. Therefore, in various aspects, the GM-MRF model is anembodiment of a model that includes more information than a conventionalMRF model.

The various methods described herein may be implemented using a medicalimaging system. For example, FIG. 6 is a block schematic diagram of anexemplary CT imaging system 300 that may be utilized to perform themethods described herein. Although the CT imaging system 300 isillustrated as a standalone imaging system, it should be realized thatthe CT imaging system 300 may form part of a multi-modality imagingsystem. For example, the multi-modality imaging system may include theCT imaging system 300 and a positron emission tomography (PET) imagingsystem, or a single photon emission computed tomography (SPECT) imagingsystem. It should also be understood that other imaging systems capableof performing the functions described herein are contemplated as beingused.

The CT imaging system 300 includes a gantry 310 that has the X-raysource 312 that projects a beam of X-rays toward the detector array 314on the opposite side of the gantry 310. The detector array 314 includesa plurality of detector elements 316 that are arranged in rows andchannels that together sense the projected X-rays that pass through asubject, such as the subject 16 shown in FIG. 1. The imaging system 300also includes the computer 18 that receives the projection data from thedetector array 314 and processes the projection data to reconstruct animage of the subject 16. In operation, operator supplied commands andparameters are used by the computer 18 to provide control signals andinformation to reposition a motorized table 322. More specifically, themotorized table 322 is utilized to move the subject 16 into and out ofthe gantry 310. Particularly, the table 322 moves at least a portion ofthe subject 16 through a gantry opening (not shown) that extends throughthe gantry 310.

As discussed above, the detector 314 includes a plurality of detectorelements 316. Each detector element 316 produces an electrical signal,or output, that represents the intensity of an impinging X-ray beam andhence allows estimation of the attenuation of the beam as it passesthrough the subject 16. During a scan to acquire the X-ray projectiondata, the gantry 310 and the components mounted thereon rotate about acenter of rotation 340. FIG. 6 shows only a single row of detectorelements 316 (i.e., a detector row). However, the multislice detectorarray 314 includes a plurality of parallel detector rows of detectorelements 316 such that projection data corresponding to a plurality ofslices can be acquired simultaneously during a scan.

Rotation of the gantry 310 and the operation of the X-ray source 312 aregoverned by a control mechanism 342. The control mechanism 342 includesan X-ray controller 344 that provides power and timing signals to theX-ray source 312 and a gantry motor controller 346 that controls therotational speed and position of the gantry 310. A data acquisitionsystem (DAS) 348 in the control mechanism 342 samples analog data fromdetector elements 316 and converts the data to digital signals forsubsequent processing. For example, the subsequent processing mayinclude utilizing the model generating module 30 to implement thevarious methods described herein. An image reconstructor 350 receivesthe sampled and digitized X-ray data from the DAS 348 and performshigh-speed image reconstruction. The reconstructed images are input tothe computer 18 that stores the image in a storage device 352.Optionally, the computer 18 may receive the sampled and digitized X-raydata from the DAS 348 and perform various methods described herein usingthe module 30. The computer 18 also receives commands and scanningparameters from an operator via a console 360 that has a keyboard. Anassociated visual display unit 362 allows the operator to observe thereconstructed image and other data from computer.

The operator supplied commands and parameters are used by the computerto provide control signals and information to the DAS 348, the X-raycontroller 344 and the gantry motor controller 346. In addition, thecomputer 18 operates a table motor controller 364 that controls themotorized table 322 to position the subject 16 in the gantry 310.Particularly, the table 322 moves at least a portion of the subject 16through the gantry opening.

In various embodiments, the computer 18 includes a device 370, forexample, a floppy disk drive, CD-ROM drive, DVD drive, magnetic opticaldisk (MOD) device, or any other digital device including a networkconnecting device such as an Ethernet device for reading instructionsand/or data from a tangible non-transitory computer-readable medium 372,that excludes signals, such as a floppy disk, a CD-ROM, a DVD or anotherdigital source such as a network or the Internet, as well as yet to bedeveloped digital means. In another embodiment, the computer 18 executesinstructions stored in firmware (not shown). The computer 18 isprogrammed to perform functions described herein, and as used herein,the term computer is not limited to just those integrated circuitsreferred to in the art as computers, but broadly refers to computers,processors, microcontrollers, microcomputers, programmable logiccontrollers, application specific integrated circuits, and otherprogrammable circuits, and these terms are used interchangeably herein.

In the exemplary embodiment, the X-ray source 312 and the detector array314 are rotated with the gantry 310 within the imaging plane and aroundthe subject 16 to be imaged such that the angle at which an X-ray beam374 intersects the subject 16 constantly changes. A group of X-rayattenuation measurements, i.e., projection data, from the detector array314 at one gantry angle is referred to as a “view”. A “scan” of thesubject 16 comprises a set of views made at different gantry angles, orview angles, during one revolution of the X-ray source 312 and thedetector 314. In a CT scan, the projection data is processed toreconstruct an image that corresponds to a three-dimensional volumetaken of the subject 16.

Exemplary embodiments of a multi-modality imaging system are describedabove in detail. The multi-modality imaging system componentsillustrated are not limited to the specific embodiments describedherein, but rather, components of each multi-modality imaging system maybe utilized independently and separately from other components describedherein. For example, the multi-modality imaging system componentsdescribed above may also be used in combination with other imagingsystems.

As used herein, the terms “software” and “firmware” are interchangeable,and include any computer program stored in memory for execution by acomputer, including RAM memory, ROM memory, EPROM memory, EEPROM memory,and non-volatile RAM (NVRAM) memory. The above memory types areexemplary only, and are thus not limiting as to the types of memoryusable for storage of a computer program.

It is to be understood that the above description is intended to beillustrative, and not restrictive. For example, the above-describedembodiments (and/or aspects thereof) may be used in combination witheach other. In addition, many modifications may be made to adapt aparticular situation or material to the teachings of the inventionwithout departing from its scope. While the dimensions and types ofmaterials described herein are intended to define the parameters of theinvention, they are by no means limiting and are exemplary embodiments,Many other embodiments will be apparent to those of skill in the artupon reviewing the above description. The scope of the invention should,therefore, be determined with reference to the appended claims, alongwith the full scope of equivalents to which such claims are entitled. Inthe appended claims, the terms “including” and “in which” are used asthe plain-English equivalents of the respective terms “comprising” and“wherein.” Moreover, in the following claims, the terms “first,”“second,” and “third,” etc., are used merely as labels, and are notintended to impose numerical requirements on their objects. Further, thelimitations of the following claims are not written inmeans-plus-function format and are not intended to be interpreted basedon 35 U.S.C. §112, sixth paragraph, unless and until such claimlimitations expressly use the phrase “means for” followed by a statementof function void of further structure.

This written description uses examples to disclose the variousembodiments of the invention, including the best mode, and also toenable any person skilled in the art to practice the various embodimentsof the invention, including making and using any devices or systems andperforming any incorporated methods. The patentable scope of the variousembodiments of the invention is defined by the claims, and may includeother examples that occur to those skilled in the art. Such otherexamples are intended to be within the scope of the claims if theexamples have structural elements that do not differ from the literallanguage of the claims, or if the examples include equivalent structuralelements with insubstantial differences from the literal languages ofthe claims.

What is claimed is:
 1. A method of generating a model for imageprocessing, said method comprising: selecting at least one referenceimage from a plurality of reference images; partitioning the at leastone reference image into a plurality of patches; generating anindividual patch model for each of the patches, wherein the individualpatch model for each patch jointly models a patch density along withspatial structure and texture of the corresponding patch, wherein eachindividual patch model includes a mean of the corresponding patch and aninverse covariance of the corresponding patch; and generating a model ofa probability distribution for the at least one reference image usingthe individual patch models for the patches; wherein generating themodel comprises: calculating a density value for each of the patches;and merging the density values to generate a model of the referenceimage, the model including a texture and a density of the referenceimage.
 2. The method of claim 1, further comprising reconstructing oneor more images from raw data using the generated model, wherein the oneor more images comprise at least one of a two-dimensional image or athree-dimensional image.
 3. The method of claim 1, further comprisingperforming image processing on one or more images by applying thegenerated model to the one or more images.
 4. The method of claim 1,wherein the selecting comprises selecting an image volume defined by atleast some of the plurality of reference images.
 5. The method of claim1, further comprising modeling a multi-material density and a spatialtexture of the reference image using the generated model.
 6. The methodof claim 5, further comprising modeling the multi-material densityconcurrently with the spatial texture.
 7. The method of claim 1, whereinthe model includes a joint model of a density and a texture of thereference image, the method further comprising: incorporating the jointmodel into a model based iterative reconstruction (MBIR) algorithm; andreconstructing the plurality of images using the incorporated model. 8.The method of claim 1, further comprising using a mixture distributionto model the probability distribution of the patches.
 9. The method ofclaim 1, further comprising using a Gaussian mixture distribution tomodel the probability distribution of the patches.
 10. A non-transitorycomputer readable medium programmed to instruct a computer of a ComputedTomography (CT) system to: receive a user input selecting at least onereference image from a plurality of reference images; automaticallypartition the at least one reference image into a plurality of patches;generate an individual patch model for each of the patches, wherein theindividual patch model for each patch jointly models a patch densityalong with spatial structure and texture of the corresponding patch,wherein each individual patch model includes a mean of the correspondingpatch and an inverse covariance of the corresponding patch; and generatea model of a probability distribution for the at least one referenceimage using the individual patch models for the patches; whereingenerating the model comprises: calculating a density value for each ofthe patches; and merging the density values to generate a model of thereference image, the model including a texture and a density of thereference image.
 11. The non-transitory computer readable medium ofclaim 10, being further programmed to reconstruct one or more imagesfrom raw data using the generated model, wherein the one or more imagescomprise at least one of a two-dimensional image or a three-dimensionalimage.
 12. The non-transitory computer readable medium of claim 10,being further programmed to perform image processing on one or moreimages by applying the generated model to the one or more images. 13.The non-transitory computer readable medium of claim 10, being furtherprogrammed to model a multi-material density and a spatial texture ofthe reference image using the generated model.
 14. The non-transitorycomputer readable medium of claim 10, being further programmed to modelthe multi-material density concurrently with the spatial texture. 15.The non-transitory computer readable medium of claim 10, wherein themodel includes a joint model of a density and a texture of the referenceimage, the computer readable medium being further programmed to:incorporate the joint model into a model based iterative reconstruction(MBIR) algorithm; and reconstruct the plurality of images using theincorporated model.
 16. The non-transitory computer readable medium ofclaim 10, being further programmed to use a mixture distribution tomodel the probability distribution of the patches.
 17. Thenon-transitory computer readable medium of claim 10, being furtherprogrammed to use a Gaussian mixture distribution to model theprobability distribution of the patches.
 18. A computed tomography (CT)imaging system comprising: a detector configured to output x-rayattenuation information; and a processor coupled to the detector, theprocessor being configured to: receive a user input selecting at leastone reference image from a plurality of reference images; automaticallypartition the at least one reference image into a plurality of patches;generate an individual patch model for each of the patches, wherein theindividual patch model for each patch jointly models a patch densityalong with spatial structure and texture of the corresponding patch,wherein each individual patch model includes a mean of the correspondingpatch and an inverse covariance of the corresponding patch; and generatea model of a probability distribution for the at least one referenceimage using the individual patch models for the patches; whereingenerating the model comprises: calculating a density value for each ofthe patches; and merging the density values to generate a model of thereference image, the model including a texture and a density of thereference image.
 19. The CT system of claim 18, wherein the processor isfurther programmed to receive the x-ray attenuation information as rawdata and reconstruct one or more images from the raw data using thegenerated model, wherein the one or more images comprise at least one ofa two-dimensional image or a three-dimensional image.
 20. The CT systemof claim 18, wherein the processor is further programmed to performimage processing on one or more images reconstructed from the x-rayattenuation information by applying the generated model to the one ormore images.
 21. The CT system of claim 18, wherein the processor isfurther programmed to model a multi-material density and a spatialtexture of the reference image using the generated model.
 22. The CTsystem of claim 18, wherein the processor is further programmed to modelthe multi-material density concurrently with the spatial texture. 23.The CT system of claim 18, wherein the model includes a joint model of adensity and a texture of the reference image, the processor is furtherprogrammed to: incorporate the joint model into a model based iterativereconstruction (MBIR) algorithm; and reconstruct the plurality of imagesusing the incorporated model.
 24. The CT system of claim 18, wherein theprocessor is further programmed to use a Gaussian mixture distributionto model the probability distribution of the patches.